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During the 1950s–1970s, there were three geodesy professors in Sweden. Before and after that period the only such position was at KTH in Stockholm. One in the triple proposed the creation of the Nordic Geodetic Commission, which was realized in 1953 and still exists in much the same form as originally proposed.

Recently a number of geoid campaigns were performed to verify different types of geoid and quasigeoid modeling techniques. Typically, GNSS-leveling was employed as an independent method, but in some cases zenith camera astronomic deflection data were also used in astrogeodetic determinations of the geoid and/or quasigeoid. However, due to the uncertainty in the topographic density distribution data (and thereby in orthometric heights), we conclude that neither GNSS-leveling nor astrogeodetic techniques can reliably verify differences between gravimetric geoid models at several centimeter levels in rough mountainous regions. This is because much the same topographic data are used both in the gravimetric geoid models and in their verifications by geometric and/or astrogeodetic geoid models. On the contrary, this is not a problem in verifying gravimetric quasigeoid models, as they are independent of the topographic density distribution, and so is the related normal height used in GNSS-leveling.

The topographic potential bias at geoid level is the error of the analytically continued geopotential from or above the Earth’s surface to the geoid. We show that the topographic potential can be expressed as the sum of two Bouguer shell components, where the density distribution of one is spherical symmetric and the other is harmonic at any point along the normal to a sphere through the computation point. As a harmonic potential does not affect the bias, the resulting topographic bias is that of the first component, i.e. the spherical symmetric Bouguer shell. This implies that the so-called terrain potential is not likely to contribute significantly to the bias. We present three examples of the geoid bias for different topographic density distributions.

The geoid, but not the quasigeoid, is an equipotential surface in the Earth’s gravity field that can serve both as a geodetic datum and a reference surface in geophysics. It is also a natural zero-level surface, as it agrees with the undisturbed mean sea level. Orthometric heights are physical heights above the geoid,while normal heights are geometric heights (of the telluroid) above the reference ellipsoid. Normal heights and the quasigeoid can be determined without any information on the Earth’s topographic density distribution, which is not the case for orthometric heights and geoid. We show from various derivations that the difference between the geoid and the quasigeoid heights, being of the order of 5 m, can be expressed by the simple Bouguer gravity anomaly as the only term that includes the topographic density distribution. This implies that recent formulas, including the refined Bouguer anomaly and a difference between topographic gravity potentials, do not necessarily improve the result. Intuitively one may assume that the quasigeoid, closely related with the Earth’s surface, is rougher than the geoid. For numerical studies the topography is usually divided into blocks of mean elevations, excluding the problem with a non-star shaped Earth. In this case the smoothness of both types of geoid models are affected by the slope of the terrain,which shows that even at high resolutions with ultra-small blocks the geoid model is likely as rough as the quasigeoid model. In case of the real Earth there are areas where the quasigeoid, but not the geoid, is ambiguous, and this problem increases with the numerical resolution of the requested solution. These ambiguities affect also normal and orthometric heights. However, this problem can be solved by using the mean quasigeoid model defined by using average topographic heights at any requested resolution. An exact solution of the ambiguity for the normal height/quasigeoid can be provided by GNSS-levelling.

It is well known that the success in precise determinations of the gravimetric geoid height (N) and the orthometric height (H) rely on the knowledge of the topographic mass distribution. We show that the residual topographic bias due to an imprecise information on the topographic density is practically the same for N and H, but with opposite signs. This result is demonstrated both for the Helmert orthometric height and for a more precise orthometric height derived by analytical continuation of the external geopotential to the geoid. This result leads to the conclusion that precise gravimetric geoid heights cannot be validated by GNSS-levelling geoid heights in mountainous regions for the errors caused by the incorrect modelling of the topographic mass distribution, because this uncertainty is hidden in the difference between the two geoid estimators.

This article is a personal review of the development of physical geodesy during 1984-2014. The period is characterized by an intensive advance in both data and theory to meet the growing technical demands in GPS/GNSS applications and scientific needs in geoscience. As a result,many parts of theworld are nowmapped with a 1cmdetailed geoid model, and the global long- to mediumwavelengths of the gravity field and geoid are homogeneously determined to 1 mGal and 1 cm by satellite-only dedicated satellite gravity missions. The future can expect to see even higher demands for accuracy and reliability to satisfy the specifications for a pure geoid model based vertical datum.